In　recent　years,　based　on　jointly　modeling　the　mean　and　variance,　double　regression　models　are　widely　used　in　practice.　In　order　to　assess　the　effects　of　continuous　covariates　or　of　time　scales　in　a　flexible　way,　a　class　of　semiparametric　mixed-effects　double　regression　models(　SMMEDRMs)　is　considered,　in　which　we　model　the　variance　of　the　mixed　effects　directly　as　a　function　of　the　explanatory　variables.　In　this　paper,　we　propose　a　fully　Bayesian　inference　for　SMMEDRMs　on　the　basis　of　B-spline　estimates　of　nonparametric　components.　A　computational　efficient　MCMC　method　which　combines　the　Gibbs　sampler　and　Metropolis-Hastings　algorithm　is　implemented　to　simultaneously　obtain　the　Bayesian　estimates　of　unknown　parameters　and　the　smoothing　function,　as　well　as　their　standard　deviation　estimates.　Finally,　some　simulation　studies　and　a　real　example　are　used　to　illustrate　the　proposed　methodology.